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Abstract:
The Kerr nature of a compact-object-coalescence remnant can be unveiled by
observing multiple quasi-normal modes (QNMs) in the post-merger signal. Current
methods to achieve this goal rely on matching the data with a superposition of
exponentially damped sinusoids with amplitudes fitted to numerical-relativity
(NR) simulations of binary black-hole (BBH) mergers. These models presume the
ability to correctly estimate the time at which the gravitational-wave (GW)
signal starts to be dominated by the QNMs of a perturbed BH. Here we show that
this difficulty can be overcome by using multipolar inspiral-merger-ringdown
waveforms, calibrated to NR simulations, as already developed within the
effective-one-body formalism (EOBNR). We build a parameterized (nonspinning)
EOBNR waveform model in which the QNM complex frequencies are free parameters
(pEOBNR), and use Bayesian analysis to study its effectiveness in measuring
QNMs in GW150914, and in synthetic GW signals of BBHs injected in Gaussian
noise. We find that using the pEOBNR model gives, in general, stronger
constraints compared to the ones obtained when using a sum of damped sinusoids
and using Bayesian model selection, we also show that the pEOBNR model can
successfully be employed to find evidence for deviations from General
Relativity in the ringdown signal. Since the pEOBNR model properly includes
time and phase shifts among QNMs, it is also well suited to consistently
combine information from several observations --- e.g., we find on the order of
$\sim 30$ GW150914-like BBH events would be needed for Advanced LIGO and Virgo
at design sensitivity to measure the fundamental frequencies of both the
$(2,2)$ and $(3,3)$ modes, and the decay time of the $(2,2)$ mode with an
accuracy of $\lesssim 5\%$ at the $2\mbox{-}\sigma$ level, thus allowing to
test the BH's no-hair conjecture.